Re: Which one should I trust : shapiro test or qq plot?

I would prefer to look at the QQ plot.

But the important thing is if the data (in each group, or the residuals) is roughly normal, so that it does not deviate a lot from normality. Also, the central limit theorem says that sums (like in "parametric estimation") tends to be normally distributed. The way I interpret your results I believe that it is Ok to use the normal model.

Besides, there are many other parametric distributions than the normal.

Re: Which one should I trust : shapiro test or qq plot?

It is never possible to show normality. It is only possible to reject normality.

And you know from the start that a seven point Likert scale (I believe you mean Likert item) is not normally distributed, since it is discrete and has a finite range, while the normal distribution goes from minus infinity to plus infinity and it is continuous. What matters is that it is a good model, that it is somewhat bell shaped. And really that the test statistics approximately follows a t-distribution (if that is what you intend to use).